The prior art discloses various processes for determining a molecular weight distribution, for example under the name “GPC”. In the GPC process, a polymer is dissolved and applied to a porous column. The faster the column is passed through, the higher the molecular weight. The speed with which the column is passed through is thus a measure of the molecular weight distribution.
This process has the disadvantage of only being able to analyze those polymers which are soluble. The sensitivity of the process also decreases with ever greater molecular weight.
In order to overcome the disadvantage regarding the sensitivity with increasing molecular weight, the prior art proposes calculating a molecular weight distribution on the basis of physical data. Such a process has become known, inter alia, from the publication “W. Thimm et al., An analytical relation between relaxation time spectrum and molecular weight distribution, J. Rheol. 43 No. 6 (1999) 1663-1672”.
First, the complex shear modulus is measured as a function of frequency at different temperatures. For technical reasons, measurements are made at frequencies of 10−3 to 103 Hz. Reduction of the frequency below 10−3 Hz causes the measurement time to grow greatly. For example, the measurement time at 10−3 Hz is 1 hours. For apparatus reasons, measurements above 103 Hz are problematic, since intrinsic vibrations of the apparatus setup distort the result.
In order to be able to evaluate data over a relatively large frequency range irrespective of this problem, the fact that a measurement at relatively low temperatures can be converted by calculation to a measurement at relatively high frequencies is utilized. Such a conversion results in a so-called mastercurve which covers a relatively wide frequency spectrum. Two functions which characterize and reproduce the complex shear modulus with respect to frequency are then present in numerical form. One is the real part and the other the imaginary part. The real part is referred to as storage modulus and the imaginary part as loss modulus. The typical frequency range encompasses 14-20 decades, even though measurement has been effected only within the aforementioned frequency range.
According to the prior art, the so-called relaxation time spectrum is determined numerically therefrom. The numerical conversion of numerical starting data to a relaxation time spectrum is disadvantageously a so-called ill-posed problem. Errors in the starting data (measurements or values of the mastercurve) can be magnified by the conversion.
With the aid of the relaxation time spectrum and the generalized mixing rule, the distribution of the molecular weight m is determined numerically. The generalized mixing rule describes a relationship between the relaxation time spectrum h(m) and the molecular weight distribution ω(m). The relaxation time spectrum h(m) is available in numerical form. Therefore, this equation is solved numerically according to the prior art.